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# FP3 locus problem Watch

1. The line with equation y=mx-2 meets the ellipse with equation x²+4y²=16 at the points P and Q.

a) Find the midpoint M of P and Q, giving each co ordinate in terms of m,
x=16m/(1+4m2)
y=-2/(1+4m2)

b) As m varies, find in cartesian form, an equation of the locus of M
Stuck on this one.
2. (Original post by bobbricks)
The line with equation y=mx-2 meets the ellipse with equation x²+4y²=16 at the points P and Q.

a) Find the midpoint M of P and Q, giving each co ordinate in terms of m,
x=16m/(1+4m2)
y=-2/(1+4m2)
I get so one of us seems to be a factor of 2 out. I agree with the expression for

b) As m varies, find in cartesian form, an equation of the locus of M
Stuck on this one.
You have to eliminate between the expressions that you have for to find an equation for the locus in terms of .
3. (Original post by bobbricks)
The line with equation y=mx-2 meets the ellipse with equation x²+4y²=16 at the points P and Q.

a) Find the midpoint M of P and Q, giving each co ordinate in terms of m,
x=16m/(1+4m2)
y=-2/(1+4m2)

b) As m varies, find in cartesian form, an equation of the locus of M
Stuck on this one.
As you see from the coordinates of the M

x=-8m*y -> y= ...... gives the equation of the locus of M (which will be a line)
4. (Original post by ztibor)
As you see from the coordinates of the M

x=-8m*y -> y= ...... gives the equation of the locus of M (which will be a line)
Which line? I get an ellipse.
5. Okay, thanks guys! I've managed to get an equation of an ellipse though (which seems to be the correct answer)
6. (Original post by ztibor)
As you see from the coordinates of the M

x=-8m*y -> y= ...... gives the equation of the locus of M (which will be a line)

(Original post by atsruser)
Which line? I get an ellipse.
May I join in?

I have not done it but I expect an ellipse.

If the parametrics are correct divide the equations to get m = -x/(8y) and substitute into the easier equation
7. (Original post by atsruser)
I get so one of us seems to be a factor of 2 out. I agree with the expression for

You have to eliminate between the expressions that you have for to find an equation for the locus in terms of .
Your value for x is correct

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